Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Module Ottimizzazione Combinatoria

Being able to evaluate the general complexity of combinatorial optimization problems. Being able to formulate them as 0-1 linear programming. Know basic primal-dual relations. Know elementary matroid theory, dynamic programming. Have the notion and know the main properties of unimodular matrices. Have basic notions on algorithm and problem complexity. Know standard algorithms for spanning tree, bipartite matching, shortest path. Know heuristics for the TSP and Knapsack. Know general implicit enumeration, LP based algorithms (branch-and-bound)

Understand the difference between an “easy” and a “hard” problem. Evaluate the complexity of an algorithm and, for simple cases, of a problem. Be able to recognize whether a matrix is, or is not, totally unimodular. Solve by standard algorithms the spanning tree, bipartite matching, knapsack, optimal path, travelling salesman problem. Formulate combinatorial optimization problems, or binary optimization problems derived from applications, as 0-1 linear programming.

Understand when a problem has the shape of a matroid and what is the advantage. Know what is the advantage of a totally unimodular matrix. Decide when it is convenient to use dynamic programming. Realize the limits of heuristics.

Prove rigorously a simple theorem. Prove or disprove (by counterexample) a simple conjecture. Understand the role played by combinatorial optimization in applications.

Acquire autonomy in modeling and algorithmic choices for problems related to complex decision-making

Be able to hold a conversation and to read texts on topics related to the modeling of decision problems and Linear Programming

Acquire the ability of upgrading flexible knowledge and skills in the field of Optimization and related problems that arise in various areas, such as mathematics, computer science and management science

Teaching Methods

Assessment Methods and Criteria

Module Ottimizzazione Combinatoria: written test, oral testModule Ricerca Operativa: 1. paper test consisting of various exercises (problem formulation, insights about algebraic or geometric problems properties, problem solution by know algorithms)
2. oral test about theoretical topics; this is accessible only for the students who earned a passing grade at the paper test; NOTE: a sufficient paper test allows the student only for the oral at the same date, but NOT for next dates.
3. A mid-term test is also planned: a positive grade to it allows the student to skip the corresponding topics in the final test.